Week 3 - Daily Quiz

A number is increased by 4, the result is doubled, and then 4 is added again to give an answer of 84. What is the number?

• 28

• 40

• 32

• 36

The sum of 5 consecutive odd numbers is 95. What is the smallest of these numbers?

• 15

• 17

• 19

• 21

Answer explanation

Let the smallest odd number be x. Since odd numbers increase by 2 each time, the next ones are x + 2, x + 4, x + 6, x + 8. Their sum is:

x + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 5x + 20

We’re told the sum is 95, so:

5x + 20 = 95
5x = 75
x = 15

So, the smallest number is 15.

How many goats and chickens are in the yard if there are 41 animals and 112 legs?

• 20 goats, 21 chickens

• 30 goats, 11 chickens

• 19 goats, 22 chickens

• 15 goats, 26 chickens

Answer explanation

Let G be goats and C be chickens.

We know that:
G + C = 41 (total animals)
4G + 2C = 134 (total legs)

The first equation in terms of C: C = 41 - G
Plug into second equation:
4G + 2(41 - G) = 134
4G + 82 - 2G = 134
2G = 52 → G = 26 → C = 15
That means that there are 15 goats and 26 chickens.

What is the value of 3x+5 when x=2?

• 11

• 9

• 7

• 8

Answer explanation

To find the value of 3x + 5 when x = 2, substitute 2 for x: 3(2) + 5 = 6 + 5 = 11. Therefore, the correct answer is 11.

Luna Park charges $4x+10 for entry, where x is the number of rides someone goes on. If Miles Morales goes on 6 rides, what is the total amount he will spend at the park?

• $34

• $40

• $24

• $30

Answer explanation

To find the total cost for 6 rides, substitute x with 6 in the expression $4x + 10: $4(6) + 10 = $24 + 10 = $34. Thus, the total amount Miles spends is $34.

Snoopy has 3r+5b red marbles and 4r+2b blue marbles. What is the simplified expression for the total number of marbles?

• 5r + 7b

• 7(r + b)

• 8(r + b)

• 6(r + b)

Answer explanation

To find the total number of marbles, add the red and blue marbles: (3r + 5b) + (4r + 2b) = 7r + 7b. This can be factored as 7(r + b), making it the correct choice.

Sophia has 5 more than twice the number of pencils as James. If Sophia has 15 pencils, how many pencils does James have?

• 5

• 3

• 7

• 10

Answer explanation

Let J be the number of pencils James has. The equation is 15 = 2J + 5. Solving for J gives 2J = 10, so J = 5. Therefore, James has 5 pencils.

A rectangular garden has a length of 2x+4 meters and a width of x+3 meters. What is the expression for the perimeter of the garden?

• 8x + 14

• 4x + 14

• 6x + 10

• 6x + 14

Answer explanation

To find the perimeter of a rectangle, use the formula P = 2(length + width). Here, length = 2x + 4 and width = x + 3. Thus, P = 2((2x + 4) + (x + 3)) = 2(3x + 7) = 6x + 14. The correct answer is 6x + 14.

If x = −3, what is the value of 2x² - 4x +1?

• -5

• 10

• 20

• 31

Answer explanation

Substituting x = -3 into the expression: 2(-3)² - 4(-3) + 1 = 2(9) + 12 + 1 = 18 + 12 + 1 = 31. Thus, the value is 31.

The sum of three consecutive even numbers is 48. What is the largest of these numbers?

• 22

• 18

• 16

• 20

Answer explanation

Let the three consecutive even numbers be x, x+2, and x+4. Their sum is x + (x+2) + (x+4) = 3x + 6. Setting this equal to 48 gives 3x + 6 = 48, leading to 3x = 42, so x = 14. The largest number is 14 + 4 = 18.